Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session D37: Focus Session: Electro-Hydro-Dynamics of Drops, Vesicles and Membranes I |
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Chair: David Saintillan, University of California - San Diego Room: Sheraton Back Bay A |
Sunday, November 22, 2015 2:10PM - 2:23PM |
D37.00001: The fate of electrospray drops Osman Basaran, Robert Collins, Krishnaraj Sambath, Michael Harris Drops subjected to strong electric fields emit thin fluid jets from conical structures (Taylor cones) that form at their surfaces. Such behavior has practical, e.g. electrospray mass spectrometry, and fundamental, e.g. raindrops in thunderclouds, implications. Theoretical analysis of the temporal development of such EHD tip-streaming phenomena is challenging given the large disparity in length scales between the macroscopic drops and the microscopic jets. Furthermore, there exist conflicting theories and measurements on the size and charge of these small electrospray droplets. We use theory and simulation to show that conductivity can be tuned to yield three scaling regimes for droplet radius and charge, a finding missed by previous studies. The amount of charge Q that electrospray droplets carry determines whether they are coulombically stable and charged below the Rayleigh limit of stability R or are unstable and hence prone to further explosions once formed. Previous experiments reported droplet charge values ranging from 1/10th to in excess of R. Simulations unequivocally show that electrospray droplets are coulombically stable at the instant they are created and that there exists a universal scaling law for droplet charge, Q=0.44 R. [Preview Abstract] |
Sunday, November 22, 2015 2:23PM - 2:36PM |
D37.00002: Electro-rotation of drops at large electric Reynolds numbers Ehud Yariv, Itzchak Frankel We analyze spontaneous electrohydrodynamic rotation of drops under a uniform electric field by applying the Taylor-Melcher leaky-dielectric model to a two-dimensional system. The dimensionless problem is governed by the ratios of electric conductivities, dielectric permittivities and shear viscosities in the respective drop- and suspending liquid phases as well as the electric Reynolds number R$_e$ quantifying surface-charge convection. We address the asymptotic limit of large R$_e$ where the dominant balance in the boundary conditions results in the flow scaling as R$_e^{-1/2}$. This flow is governed by a nonlinear boundary-value problem which does not admit a fore-aft symmetric solution, thus necessitating drop rotation. This problem, which is invariant to the inversion of the velocity field, is transformed into a universal one, independent of the conductivity and permittivity ratios. Thermodynamic arguments reveal that a solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. Under these conditions, the rescaled angular velocity is obtained as a function of the viscosity ratio. Comparable numerical solutions, obtained using the exact equations, indeed collapse at large R$_e$ upon the asymptotic universal solution. [Preview Abstract] |
Sunday, November 22, 2015 2:36PM - 2:49PM |
D37.00003: Electrohydrodynamic deformation of drops and bubbles at large Reynolds numbers Ory Schnitzer In Taylor's theory of electrohydrodynamic drop deformation by a uniform electric field, inertia is neglected at the outset, resulting in fluid velocities that scale with $E^2$, $E$ being the applied-field magnitude. When considering strong fields and low viscosity fluids, the Reynolds number predicted by this scaling may actually become large, suggesting the need for a complementary large-Reynolds-number analysis. Balancing viscous and electrical stresses reveals that the velocity scales with $E^{4/3}$. Considering a gas bubble, the external flow is essentially confined to two boundary layers propagating from the poles to the equator, where they collide to form a radial jet. Remarkably, at leading order in the Capillary number the unique scaling allows through application of integral mass and momentum balances to obtain a closed-form expression for the $O(E^2)$ bubble deformation. Owing to a concentrated pressure load at the vicinity of the collision region, the deformed profile features an equatorial dimple which is non-smooth on the bubble scale. The dynamical importance of internal circulation in the case of a liquid drop leads to an essentially different deformation mechanism. This is because the external boundary layer velocity attenuates at a short distance from the interface, while the internal boundary-layer matches with a Prandtl-Batchelor (PB) rotational core. The dynamic pressure associated with the internal circulation dominates the interfacial stress profile, leading to an $O(E^{8/3})$ deformation. The leading-order deformation can be readily determined, up to the PB constant, without solving the circulating boundary-layer problem. To encourage attempts to verify this new scaling, we shall suggest a favourable experimental setup in which inertia is dominant, while finite-deformation, surface-charge advection, and gravity effects are negligible. [Preview Abstract] |
Sunday, November 22, 2015 2:49PM - 3:02PM |
D37.00004: The relaxation of a prolate leaky dielectric drop in a uniform DC electric field Aditya Khair, Javier Lanauze, Lynn Walker We quantify the relaxation of a prolate leaky dielectric drop upon removal of a uniform DC electric field. Experiments consisting of a castor oil drop suspended in a silicone oil are compared against boundary integral simulations that account for transient charging of the interface. Charge relaxation causes a marked asymmetry in the drop evolution during deformation and relaxation. In particular, during relaxation a prolate to oblate shape transition is observed before the drop recovers its equilibrium spherical shape. Furthermore, the high field strengths utilized in the experiments yield a fast drop relaxation in comparison with the transient development towards the steady deformation. The storage and release of capacitive energy and capillary energy is then quantified during deformation and relaxation, respectively. Finally, we present computational results for a drop that does not relax back to its initial spherical shape upon removal of the field; rather, the drop breaks up. [Preview Abstract] |
Sunday, November 22, 2015 3:02PM - 3:15PM |
D37.00005: Nonlinear electrohydrodynamics of leaky dielectric drops in the Quincke regime: Numerical simulations Debasish Das, David Saintillan The deformation of leaky dielectric drops in a dielectric fluid medium when subject to a uniform electric field is a classic electrohydrodynamic phenomenon best described by the well-known Melcher-Taylor leaky dielectric model. In this work, we develop a three-dimensional boundary element method for the full leaky dielectric model to systematically study the deformation and dynamics of liquid drops in strong electric fields. We compare our results with existing numerical studies, most of which have been constrained to axisymmetric drops or have neglected interfacial charge convection by the flow. The leading effect of convection is to enhance deformation of prolate drops and suppress deformation of oblate drops, as previously observed in the axisymmetric case. The inclusion of charge convection also enables us to investigate the dynamics in the Quincke regime, in which experiments exhibit a symmetry-breaking bifurcation leading to a tank-treading regime. Our simulations confirm the existence of this bifurcation for highly viscous drops, and also reveal the development of sharp interfacial charge gradients driven by convection near the drop's equator. [Preview Abstract] |
Sunday, November 22, 2015 3:15PM - 3:28PM |
D37.00006: Simulations of particle structuring driven by electric fields Yi Hu, Petia Vlahovska, Michael Miksis Recent experiments (Ouriemi and Vlahovska, 2014) show intriguing surface patterns when a uniform electric field is applied to a droplet covered with colloidal particles. Depending on the particle properties and the electric field intensity, particles organize into an equatorial belt, pole-to-pole chains, or dynamic vortices. Here we present 3D simulations of the collective particle dynamics, which account for electrohydrodynamic flow and dielectrophoresis of particles. In stronger electric fields, particles are expected to undergo Quincke rotation and impose disturbance to the ambient flow. Transition from ribbon-shaped belt to rotating clusters is observed in the presence of the rotation-induced hydrodynamical interactions. Our results provide insight into the various particle assembles discovered in the experiments. [Preview Abstract] |
Sunday, November 22, 2015 3:28PM - 3:41PM |
D37.00007: Electrohydrodynamic Displacement of Polarizable Liquid Interfaces in an Alternating Current Electric Field Zachary Gagnon In this work, we investigate Maxwell-Wagner polarization at electrically polarizable liquid interfaces. An AC electric field is applied across a liquid electrical interface created between two co-flowing microfluidic fluid streams with different electrical properties. When potentials as low as 2 volts are applied, we observe a frequency dependent interfacial displacement that is dependent on the relative differences in the electrical conductivity and dielectric constant between the two liquids. At low frequency this deflection is dependent on electrical conductivity, and only depends on dielectric constant at high frequency. At intermediate frequencies, we observe a crossover that is independent of applied voltage, sensitive to both fluid electrical properties, and where no displacement is observed. An analytical polarization model is presented that predicts the liquid interfacial crossover frequency, the dependence of interfacial displacement on liquid electrical conductivity and dielectric constant, and accurately scales the interface displacement measurements. The results show that liquid interfaces are capable of polarizing under AC electric fields and being precisely deflected in a direction and magnitude that is dependent on the applied electric field frequency. [Preview Abstract] |
Sunday, November 22, 2015 3:41PM - 3:54PM |
D37.00008: Fluctuation and dynamics of a lipid bilayer membrane under an electric field Yuan-Nan Young, Michael Miksis, Petia Vlahovska Membrane fluctuation and dynamics under an electric field is investigated, and results show that the membrane instability and dynamics depend not only on the mismatch in conductivity and permittivity between the bulk fluids, but also on the membrane charging time. In addition, the (entropic) membrane tension is found to depend on the electric field. Lubrication theory is utilized to examine the nonlinear dynamics of a planar lipid bilayer membrane with and without electrokinetics. [Preview Abstract] |
Sunday, November 22, 2015 3:54PM - 4:07PM |
D37.00009: Shape fluctuations of a giant lipid vesicle in an external electric field Nico Fricke, Petia Vlahovska We experimentally study the influence of an applied electric field on the physical properties of lipid bilayer membranes. Global and regional analyses of the shape fluctuations of a giant quasi-spherical vesicle (``flicker spectroscopy'') are used to infer membrane tension, and bending rigidity from a time series of microscope images. The parameters of the electric field (frequency and amplitude) are chosen such that there is no global vesicle deformation, and hence any renormalization of the tension and bending rigidity arise only from electric stress in the membrane. Using this approach we examine the effect of the electrotension on the main phase transition temperature of lipid membranes, where we observe that increasing field strength decreases, albeit slightly (about 0.1K), the melting temperature [Preview Abstract] |
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